Vehicle control method and apparatus

ABSTRACT

The present disclosure relates to a method of generating a target operational speed band (53; 63; 67) for a host vehicle (1) travelling along a route. A first time-dependent obstacle (15-n, 18-n) is identified at a first location on the route. The first time-dependent obstacle (15-n, 18-n) is identified as hindering progress of the host vehicle (1) during a first time period (11). The first time-lin dependent obstacle (15-n, 18-n) is defined in a two-dimensional speed against distance map (50, 60). A first speed trajectory (51, 52; 61; 65, 66) is determined from a first point to a second point within the two-dimensional speed against distance map (50, 60). The second point represents the first location on the route and the determined first speed trajectory (51, 52; 61; 65, 66) represents the host vehicle (1) arriving at the first location at a first arrival time. The target operational speed band (53; 63; 67) is determined such that the first speed trajectory (51, 52; 61; 65, 66) forms one of an upper limit and a lower limit of the target operational speed band (53; 63; 67). The first arrival time is outside said first time period (11). The present disclosure also relates to a controller (2) for generating a target operational speed band (53; 63; 67); and to a vehicle (1).

TECHNICAL FIELD

The present disclosure relates to a vehicle control method andapparatus. More particularly, but not exclusively, the presentdisclosure relates to a method of generating a target operational speedband for a host vehicle; and to a controller for generating a targetoperational speed band for a host vehicle. The present disclosure alsorelates to a vehicle incorporating a controller; and to a non-transitorycomputer-readable medium.

BACKGROUND

Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V)(collectively V2X) technologies are expected to become the norm in thecoming decade. This presents new opportunities for predictive energymanagement strategies since the amount of available information aboutthe vehicle environment is increasing beyond what is available fromin-vehicle sensors. From the point of view of energy managementstrategy, this provides significant opportunities in the ability toanticipate future events and therefore to adapt the vehicle speed andpropulsion system usage to improve energy efficiency. An example of howV2I information can be used for energy savings is when a traffic lightcommunicates its current and future states to approaching vehicles. Thisallows approaching vehicles to adapt their approach speed profile so asto potentially avoid stopping at the traffic light, thus saving energyand increasing driver comfort. An example of how V2V information can beused for energy savings is when vehicles ahead of the host vehiclecommunicate their movements to other vehicles around them. For instance,if the host vehicle is approaching a congested area, it could anticipatethe congestion and adapt its approach speed and propulsion system usageto improve energy efficiency, for example by increasing the amount ofvehicle coasting and decreasing the use of friction brakes. Thechallenge is how to take full advantage of these new opportunities. Analgorithm that calculates the desired target operational speed band andoptionally also a propulsion system management strategy for differentscenarios would be advantage.

SUMMARY OF THE INVENTION

Aspects of the present invention relate to a method, a vehicle and to anon-transitory computer-readable medium as claimed in the appendedclaims.

According to a further aspect of the present invention there is provideda method of generating a target operational speed band for a hostvehicle travelling along a route, the method comprising:

-   -   identifying a first time-dependent obstacle at a first location        on the route, the first time-dependent obstacle being identified        as hindering progress of the host vehicle during a first time        period;    -   defining the first time-dependent obstacle in a two-dimensional        speed against distance map;    -   determining a first speed trajectory from a first point to a        second point within the two-dimensional speed against distance        map, the second point representing the first location on the        route and the determined first speed trajectory representing the        host vehicle arriving at the first location at a first arrival        time; and    -   determining the target operational speed band such that the        first speed trajectory forms one of an upper limit and a lower        limit of the target operational speed band;    -   wherein said first arrival time is outside said first time        period. The speed of the host vehicle may be controlled in        dependence on the target operational speed band. The target        operational speed band may define a speed range for the host        vehicle. At least in certain embodiments, this may improve        operating efficiency of the vehicle and/or reduce a time        required to complete a trip.

Alternatively, or in addition, the method may comprise determining asecond time period when the first time-dependent obstacle is identifiedas not hindering progress of the host vehicle. The target operationalspeed band may be determined such that the host vehicle arrives at thefirst location within the second time period.

The method may comprise outputting a target speed trajectory. The targetspeed trajectory may be partially or completely contained within thetarget operational speed band.

The first speed trajectory may be generated for a first accelerationlimit of the host vehicle.

The first speed trajectory may form a lower limit of the targetoperational speed band. A cost penalty may be applied to a target speedtrajectory which is less than the first speed trajectory.

The first speed trajectory may form an upper limit of the targetoperational speed band. A cost penalty may be applied to a target speedtrajectory which is greater than the first speed trajectory.

The method may comprise determining a cost of a target speed trajectory.The cost may be determined by applying an acceleration cost penalty inrespect of each portion of the target speed trajectory having a greaterpositive acceleration than a predefined positive acceleration thresholdand/or a greater negative acceleration than a predefined negativeacceleration threshold.

The method may comprise identifying a second time period during whichthe first time-dependent obstacle permits substantially unhinderedprogress of the host vehicle. The target operational speed band may bedetermined such that the first arrival time is inside said second timeperiod.

The method may comprise determining a second speed trajectory from afirst point to a second point within the two-dimensional speed againstdistance map, the second point representing the first location on theroute and the determined first speed trajectory representing the hostvehicle arriving at the first location at a second arrival time. Thetarget operational speed band may be determined such that the secondspeed trajectory forms the other of the upper limit and the lower limitof the target operational speed band. The second arrival time may beoutside the first time period.

The first speed trajectory may be generated for a first accelerationlimit of the host vehicle.

The first obstacle may comprise a target vehicle travelling along atleast a portion of the route. The first time period may comprise a timeperiod during which the target vehicle is predicted as travelling on asection of the route identified as being unfavourable for performing anovertaking manoeuvre.

The method may comprise determining a second speed trajectory from thefirst point to the second point within the two-dimensional speed againstdistance map. The second speed trajectory may be calculated such thatthe host vehicle arrives at the second location at a second arrivaltime. The second speed trajectory may form the other of the upper limitand the lower limit of the target operational speed band.

The second arrival time may comprise a time that the target vehicle ispredicted to arrive at the second location. The second location mayrepresent an end of the section of the route identified as beingunfavourable for performing an overtaking manoeuvre.

The second time period may comprise a time period during which thetarget vehicle is predicted as travelling on a section of the routeidentified as being favourable for performing an overtaking manoeuvre.

The method may comprise identifying a speed limit applicable for atleast a part of the route between the current position of the hostvehicle and the first location. The speed limit may define at least aportion of the upper limit of the target operational speed band.

The method may comprise identifying a plurality of obstacles on theroute. The target operational speed band may be determined in respect ofeach obstacle identified on the route. A weighting may be applied to thecalculation of each target operational speed band in dependence on thecalculation performed in respect of at least one other obstacleidentified on the route. The first arrival time for arriving at thefirst obstacle may be determined in dependence on an arrival time of thehost vehicle at one or more other obstacle identified on the route.

According to a further aspect of the present invention there is provideda non-transitory computer-readable medium having a set of instructionsstored therein which, when executed, cause a processor to perform themethod described herein.

According to a further aspect of the present invention there is provideda controller for generating a target operational speed band for a hostvehicle travelling along a route, the controller comprising:

-   -   processing means for receiving an input to identify a first        time-dependent obstacle at a first location on the route, the        first time-dependent obstacle being identified as hindering        progress of the host vehicle during a first time period; and    -   memory means connected to the processing means;    -   wherein the processing means is configured to:        -   define the first time-dependent obstacle in a            two-dimensional speed against distance map;        -   determine a first speed trajectory from a first point to a            second point within the two-dimensional speed against            distance map, the second point representing the first            location on the route and the determined first speed            trajectory representing the host vehicle arriving at the            first location at a first arrival time, the first arrival            time being outside the first time period; and        -   generate the target operational speed band;        -   wherein the first speed trajectory forms one of an upper            limit and a lower limit of the target operational speed            band.

Alternatively, or in addition, the processor may be configured todetermine a second time period when the first time-dependent obstacle isidentified as not hindering progress of the host vehicle. The targetoperational speed band may be determined such that the host vehiclearrives at the first location within the second time period.

The processing means may be in the form of a processor, such as anelectronic processor. The memory means may be in the form a memorydevice.

The processing means may be configured to output a target speedtrajectory. The target speed trajectory may be partially or completelycontained within the target operational speed band.

The first speed trajectory may be generated for a first accelerationlimit of the host vehicle.

The first speed trajectory may form the lower limit of the targetoperational speed band. A cost penalty may be applied to a target speedtrajectory which is less than the first speed trajectory.

The first speed trajectory may form the upper limit of the targetoperational speed band. A cost penalty may be applied to a target speedtrajectory which is greater than the first speed trajectory.

The processing means may be configured to determine a cost of a targetspeed trajectory. The cost may be determined by applying an accelerationcost penalty in respect of each portion of the target speed trajectoryhaving a greater positive acceleration than a predefined positiveacceleration threshold and/or a greater negative acceleration than apredefined negative acceleration threshold.

The processing means may be configured to identify a second time periodduring which the first time-dependent obstacle permits substantiallyunhindered progress of the host vehicle. The target operational speedband may be determined such that the first arrival time is inside saidsecond time period.

The processing means may be configured to determine a second speedtrajectory from a first point to a second point within thetwo-dimensional speed against distance map, the second pointrepresenting the first location on the route and the determined firstspeed trajectory representing the host vehicle arriving at the firstlocation at a second arrival time.

The target operational speed band may be determined such that the secondspeed trajectory forms the other of the upper limit and the lower limitof the target operational speed band. The second arrival time may beoutside said first time period.

The first speed trajectory may be generated for a first accelerationlimit of the host vehicle.

The first obstacle may comprise a target vehicle travelling along atleast a portion of the route. The first time period may comprise a timeperiod during which the target vehicle is predicted as travelling on asection of the route identified as being unfavourable for performing anovertaking manoeuvre.

The processing means may be configured to determine a second speedtrajectory from the first point to the second point within thetwo-dimensional speed against distance map, the second speed trajectorybeing calculated such that the host vehicle arrives at the secondlocation at a second arrival time. The second speed trajectory may formthe other of the upper limit and the lower limit of the targetoperational speed band.

The second arrival time may comprise a time that the target vehicle ispredicted to arrive at the second location. The second location mayrepresent an end of the section of the route identified as beingunfavourable for performing an overtaking manoeuvre.

The second time period may comprises a time period during which thetarget vehicle is predicted as travelling on a section of the routeidentified as being favourable for performing an overtaking manoeuvre.

The processing means may be configured to identify a speed limitapplicable for at least a part of the route between the current positionof the host vehicle and the first location, wherein the speed limitdefines at least a portion of the upper limit of the target operationalspeed band.

The processing means may be configured to:

-   -   identify a plurality of obstacles on the route; and    -   generate a target operational speed band in respect of each        obstacle identified on the route.

The processing means may be configured to apply a weighting to thecalculation of each target operational speed band in dependence on thecalculation performed in respect of at least one other obstacleidentified on the route.

The first arrival time for arriving at the first obstacle may bedetermined in dependence on an arrival time of the host vehicle at oneor more other obstacle identified on the route.

Any control unit or controller described herein may suitably comprise acomputational device having one or more electronic processors. Thesystem may comprise a single control unit or electronic controller oralternatively different functions of the controller may be embodied in,or hosted in, different control units or controllers. As used herein theterm “controller” or “control unit” will be understood to include both asingle control unit or controller and a plurality of control units orcontrollers collectively operating to provide any stated controlfunctionality. To configure a controller or control unit, a suitable setof instructions may be provided which, when executed, cause said controlunit or computational device to implement the control techniquesspecified herein. The set of instructions may suitably be embedded insaid one or more electronic processors. Alternatively, the set ofinstructions may be provided as software saved on one or more memoryassociated with said controller to be executed on said computationaldevice. The control unit or controller may be implemented in softwarerun on one or more processors. One or more other control unit orcontroller may be implemented in software run on one or more processors,optionally the same one or more processors as the first controller.Other suitable arrangements may also be used.

Within the scope of this application it is expressly intended that thevarious aspects, embodiments, examples and alternatives set out in thepreceding paragraphs, in the claims and/or in the following descriptionand drawings, and in particular the individual features thereof, may betaken independently or in any combination. That is, all embodimentsand/or features of any embodiment can be combined in any way and/orcombination, unless such features are incompatible. The applicantreserves the right to change any originally filed claim or file any newclaim accordingly, including the right to amend any originally filedclaim to depend from and/or incorporate any feature of any other claimalthough not originally claimed in that manner.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments of the present invention will now be described,by way of example only, with reference to the accompanying figures, inwhich:

FIG. 1 shows a schematic representation of a host vehicle incorporatinga controller in accordance with an embodiment of the present invention;

FIG. 2 shows a schematic representation of the integration of thecontroller shown in FIG. 1 with vehicle systems;

FIG. 3 shows a schematic representation of the communication between thehost vehicle and surrounding infrastructure and target vehicles;

FIG. 4 shows a schematic representation of the architecture of thecontroller 2 shown in FIG. 1;

FIG. 5 illustrates the operation of a static speed constraintscalculator shown in FIG. 4;

FIG. 6 illustrates a rule-based model for predicting the speed of atarget vehicle;

FIG. 7A shows a two-dimensional optimization grid representing speedconstraints due to a traffic control signal;

FIG. 7B shows a three-dimensional optimization grid representing speedconstraints due to a traffic control signal;

FIG. 8 shows a two-dimensional optimization grid for determining atarget operational speed band associated with a traffic control signal;

FIG. 9 shows a two-dimensional optimization grid for determining atarget operational speed band associated with a target vehicle in afirst scenario; and

FIG. 10 shows a two-dimensional optimization grid for determining atarget operational speed band associated with a target vehicle in asecond scenario.

DETAILED DESCRIPTION

A host vehicle 1 comprising a controller 2 in accordance with anembodiment of the present invention will now be described with referenceto the accompanying figures. The controller 2 is configured to determinea target operational speed band of the host vehicle 1 in order toimprove operating efficiency and/or to reduce journey time. The hostvehicle 1 is a road vehicle, such as an automobile. It will beunderstood that the controller 2 may be implemented in other vehicletypes, such as a utility vehicle, a sports utility vehicle (SUV), anoff-road vehicle, etc.

As described herein, the controller 2 is configured to implement adynamic programming algorithm for controlling the target operationalspeed of the host vehicle 1 as it travels along a route R (illustratedin FIG. 3). The control algorithm may be implemented as part of anautonomous control function, for example comprising one or more of thefollowing: Adaptive Cruise Control (ACC), Intelligent Cruise Control(ICC), Green Light Optimized Speed Advisory (GLOSA), and Traffic JamAssist (TJA). Alternatively, or in addition, the algorithm may be usedto coach a driver of the host vehicle 1 to follow a target operationalspeed or to remain with a target operational speed band, for exampleindicating when to lift off an accelerator pedal or when to change gear.

The host vehicle 1 in the present embodiment comprises a Plug-in HybridElectric Vehicle (PHEV) having a parallel hybrid system. The hostvehicle 1 comprises an internal combustion engine (ICE) 3, a BeltIntegrated Starter Generator (BISG) 4 and an Electric Rear Axle Drive(ERAD) 5. A traction battery 6 is provided for supplying electricalenergy to the ERAD 5. The traction battery 6 is a high voltage (HV)battery in the present embodiment. The host vehicle 1 has a front axle 7and a rear axle 8. The ICE 3 and the BISG 4 are configured selectivelyto output a traction torque to the front axle 7 to drive first andsecond wheels W1, W2. The ERAD 5 is configured to output a tractiontorque to the rear axle 8 to drive third and fourth wheels W3, W4. TheICE 3 is permanently connected to the BISG 4. The ICE 3 comprises acrankshaft 9 which is mechanically connected to a torque converter (notshown) which in turn is connected to a multi-speed transmission 11. Adisconnect clutch 10 is provided for selectively disconnecting thecrankshaft 9 from the transmission 11. As described herein, a torquedemand T_(wh,drv) is generated by an autonomous or semi-autonomousvehicle control system. The parallel hybrid system is operable in aplurality of hybrid powertrain modes to deliver the torque demandT_(wh,drv). The hybrid powertrain modes comprise selectively operatingone or more of the ICE 3, the BISG 4 and the ERAD 5 to deliver thetorque demand T_(wh,drv). The ERAD 5 may output a positive tractiontorque T_(wh,erad) to propel the host vehicle 1; or a negative tractiontorque T_(wh,erad) to regenerate energy for recharging the tractionbattery 6. The BISG 4 may output a positive traction torque T_(wh,misg)to provide a torque assist for the ICE 3; or may output a negativetraction torque to perform torque charging of the traction battery 6.When referring to power, torque, and speed signals, the subscript wh isused herein to indicate the wheel frame of reference; and the subscriptwh is omitted to denote an actuator frame of reference. It will beunderstood that the controller 2 may be implemented in other drivetrainconfigurations, for example the ERAD 5 may be omitted. Alternatively,the controller 2 could be used in an Electric Vehicle (EV) which doesnot include an internal combustion engine.

Controller Architecture & Data Processing Functions

As illustrated in FIG. 2, the controller 2 comprises processing means inthe form of a processor 12. The processor 12 is connected memory meansin the form of a system memory 13. A set of computational instructionsis stored on the system memory 13 and, when executed, the computationalinstructions cause the processor 12 to perform the method(s) describedherein. The processor 12 is configured to receive a first electricalinput signal SIN1 from a transceiver 14. The transceiver 14 isconfigured to communicate with one or more target vehicle 15-n (wherethe suffix n differentiates between different target vehicles) proximalto the host vehicle 1 or along the route R of the host vehicle 1; thisform of communication is referred to herein as Vehicle-2-Vehicle (V2V)communication. Alternatively, or in addition, the transceiver 14 isconfigured to communicate with infrastructure, such as one or moretraffic control signals 18-n (where the suffix n differentiates betweendifferent traffic control signals); this form of communication isreferred to herein as Vehicle-2-Infrastructure (V2I) communication. TheV2V and V2I communication are collectively referred to as V2Xcommunication.

The processor 12 is configured to receive a second electrical inputsignal SIN2 from at least one vehicle sensor 16 provided on-board thehost vehicle 1. The at least one vehicle sensor 16 in the presentembodiment comprises a forward-looking radar 16 provided on the hostvehicle 1. The processor 12 is configured to receive a third electricalinput signal SIN3 from a navigation system 17 to determine a geospatiallocation of the host vehicle 1. The processor 12 may implement a routeplanning function to determine the route R, for example to plan theroute from a current position of the host vehicle 1 to a user-specifieddestination. The processor 12 may access geographic map data stored onthe system memory 13 to implement the route planning function. Thegeographic map data may, for example, comprise a road network.Alternatively, the route planning may be performed by a separate controlunit, for example integrated into the navigation system 17.

The target vehicle 15-n may hinder or impede progress of the hostvehicle 1 depending on where the host vehicle 1 encounters the targetvehicle 15-n. The host vehicle 1 may be hindered if the target vehicle15-n is encountered on a section of the current route R which isunfavourable for performing an overtaking manoeuvre, but may continuesubstantially unhindered if the target vehicle 15-n is encountered on asection of the current route R which is favourable for performing anovertaking manoeuvre, for example a section of road or highway havingmultiple lanes. The location where the host vehicle 1 encounters thetarget vehicle 15-n is a function of time and the relative speed of thehost vehicle 1 and the target vehicle 15-n. The traffic control signals18-n may hinder or impede progress of the host vehicle 1 depending onthe time when the host vehicle 1 arrives at the traffic control signals18-n. The host vehicle 1 may be hindered by the traffic control signals18-n if the host vehicle 1 arrives at the traffic control signals duringa red phase (i.e. when traffic is prohibited from proceeding). The hostvehicle 1 may continue substantially unhindered if the host vehicle 1arrives at the traffic control signals 18-n during a green phase (i.e.when traffic is allowed to proceed). favourable for performing. Thus,the target vehicle 15-n and the traffic control signals 18-2 arereferred to herein as time-dependent obstacles. Other time-dependentobstacles include, for example, a pedestrian crossing or alevel-crossing.

Vehicle Modeling

The dynamic programming algorithm uses a backward-facing quasi-staticlongitudinal vehicle model for the optimization of the vehicle speedtrajectory and the powertrain state. This model is now described in moredetail.

Vehicle Longitudinal Dynamics

In quasi-static simulations, the input variables are the vehicle speedV_(veh), the vehicle acceleration, a_(veh), and the road gradient angleθ_(road). The input variables are assumed to be constant for a shortdiscretization step, Δt. The tractive force F_(drv) required to drivethe vehicle for a given profile, is calculated by Newton's2n^(d law, expressed as:)

F _(drv) =M _(veh) a _(veh) +F _(r) +F _(a) +F _(g)   (1)

where m_(veh). In denotes the vehicle inertia mass of the vehicleincluding all rotational inertias. Friction force F_(r), the aerodynamicdrag force F_(a), and the gravitation force induced by the road gradientF_(g) are expressed in the following equations:

F _(r) =c _(r) m _(veh) g cos (θ_(road))   (2)

F _(a)=0.5ρ_(a) A _(f) c _(d) V _(veh) ²   (3)

F _(g) =m _(veh) g sin (θ_(road))   (4)

where c_(r) is the rolling friction coefficient, g is the gravitationalacceleration, ρ_(a) is the density of air, A_(f) is the vehicle'sfrontal area, and c_(d) is the aerodynamic drag coefficient. The vehiclecombined wheel torque is then calculated by the following equation:

T _(wh, drv) =F _(drv) r _(wh)   (5)

where r_(wh) is the wheel radius.

Assuming no wheel slip and that the rotational speed for all wheels isequal, the wheel speed is given by:

ω_(wh) =F _(drv) /r _(wh)   (6)

The tractive torque is distributed across the front and rear axles 7, 8according to the control input u₁∈[0,1], respectively as follows:

T _(wh, drv, rr) =T _(wh, drv) u ₁   (7)

T _(wh, drv, fr) =T _(wh, drv) (1-u ₁)   (8)

where T_(wh,drv,rr) and T_(wh,drv,fr) denote the tractive torque at therear axle 8 and the front axle 7, respectively.

Rear Axle Model

The torque T_(erad) at the output shaft of the ERAD 5 is calculated fromthe corresponding torque at the wheel, T_(wh,drv,rr) after consideringall lumped driveline losses η_(gb,erad) and transmission ratiov_(gb,erad):

$\begin{matrix}{T_{erad} = \left\{ \begin{matrix}{\frac{T_{{wh},{drv},{rr}}\eta_{{gb},{erad}}}{v_{{gb},{erad}}},{T_{{wh},{drv},{rr}} < 0}} \\{\frac{T_{{wh},{drv},{rr}}}{\eta_{{gb},{erad}}\mspace{14mu} v_{{gb},{erad}}},{T_{{wh},{drv},{rr}} \geq 0}}\end{matrix} \right.} & (9)\end{matrix}$

Similarly, the rotational speed ω_(erad) at the output shaft of the ERAD5 is expressed as:

ω_(erad)=ω_(wh) v _(gb,erad)   (10)

The electrical power of the ERAD 5, including lamped power losses of themotor and inverter are formulated in look-up maps of the form:

P _(ele, erad) =f _(loss, erad)(T _(erad),ω_(erad) ,V _(batt))   (11)

where V_(batt) is the voltage of the traction battery 6.

Front Axle Model

Similarly to the rear axle, and assuming that the torque converter is ina locked up state, the torque converter input torque T_(crnk) is givenby:

$\begin{matrix}{T_{crnk} = \left\{ \begin{matrix}{\frac{T_{{wh},{drv},{fr}}\eta_{{gb},{fr}}}{v_{{gb},{fr}}\left( \kappa_{gr} \right)},{T_{{wh},{drv},{rr}} < 0}} \\{\frac{T_{{wh},{drv},{fr}}}{\eta_{{gb},{fr}}\mspace{14mu} {v_{{gb},{fr}}\left( \kappa_{gr} \right)}},{T_{{wh},{drv},{rr}} \geq 0}}\end{matrix} \right.} & (12)\end{matrix}$

where η_(gb,fr) is the efficiency of the front axle transmission anddriveline including the losses of the torque converter. The gear ratiov_(gb,fr) is a function of the gear κ_(gr) which is determined by a gearshifting strategy:

κ_(gr) =f _(gr)(ω_(wh),T_(wh,drv,fr))   (13)

Alternatively, the gear κ_(gr) could be optimized as part of thepowertrain control. The input rotational speed ω_(crnk) of the torqueconverter is given by:

ω_(crnk)=ω_(wh) v _(gb,fr)   (14)

Given a transmission ratio v_(bisg) of the BISG 4, the engine torqueT_(eng) is expressed as:

T _(eng) =T _(crnk) =v _(bisg) T _(bisg)   (15)

where the BISG torque T_(bisg) is expressed as a function of theoptimization variable u₂ ∈ [-2,1]:

T _(bisg) =u ₂ T _(crnk)   (16)

The instantaneous fuel flow {dot over (m)}_(f) of the ICE 3 can beobtained by a steady state map which is expressed as:

{dot over (m)} _(f) =f _(f)(T _(eng),ω_(crnk))   (17)

A fully warm engine is assumed allowing the dependency to ICEcoolant/oil temperatures to be dropped. Similar to the ERAD 5, theelectrical power of the BISG 4 is formulated in look-up maps of theform:

P _(ele, bisg) =f _(ele, bisg)(T _(bisg),ω_(crnk) ,V _(batt))   (18)

Traction Battery Model

The dynamics of the traction battery 6 are considered and modelled as anequivalent circuit consisting of n_(cell) battery cells connected inseries. Each cell circuit consists of a resistance and a voltage source.Assuming the same charge and temperature, T_(hv,batt) across the batterypack, the total resistance and open voltage source are, given by thefollowing equations:

R _(hv,batt) =f _(R)(SOC, T _(hv, batt))   (19)

V _(oc,batt) =f _(v)(SOC,T _(hv, batt))   (20)

The rate of change of SOC is expressed by:

$\begin{matrix}{\overset{.}{SOC} = \frac{V_{{oc},{batt}} - \sqrt{V_{{oc},{batt}}^{2} - {4P_{batt}R_{{hv},{batt}}}}}{2R_{{hv},{batt}}\mspace{14mu} Q_{{hv},{batt}}}} & (21)\end{matrix}$

where Q_(hv,batt) is the HV battery capacity and P_(batt) is the HVbattery net power. The net traction battery power is expressed in termsof the required sum of electrical consumers:

P _(batt) =P _(ele, erad) +P _(ele, bisg) +P _(dcdc)   (22)

where P_(dcdc) represents all auxiliary power requests, i.e. DCDC andair-conditioning.

Vehicle model Constraints and Validation

The model accounts for system constraints so as to disregard anyinfeasible solutions. The constraints considered in this work includethe following:

-   -   ICE steady-state torque limits    -   ERAD and BISG torque limits    -   Driveline torque limits    -   Traction battery power and SOC limits

One or more of these constraints may be used when determiningacceleration limits of the host vehicle 1.

Predictive Control Algorithm

Optimal Control Theory & Dynamic Programming

A brief summary of the relevant control theory and mathematicalformulation of dynamic programming now follows.

Optimal Control Problem Formulation

The optimal control problem can be described by first defining adiscrete dynamic system x_(k+1) with n states x_(k), m inputs u_(k), andl exogenous inputs ω_(k). This can be stated as follows: find anadmissible control policy π={μ₀(x), μ₁(x), . . . , μ_(N-1)(x)} fork=0,1, . . . , N−1 such that the cost function (Equation 23) isminimized and the constraints (Equations 25 to 29) are satisfied.

$\begin{matrix}{\begin{matrix}\min \\{u_{k} \in U_{k}}\end{matrix}\left\{ {{g_{N}\left( x_{N} \right)} + {\Sigma_{0}^{N - 1}\mspace{14mu} {g_{k}\left( {x_{k},u_{k},\omega_{k}} \right)}}} \right\}} & (23)\end{matrix}$x _(k+1) =f _(k)(x _(k) , u _(k), ω_(k))   (24)

x_(k) ∈ X_(k)⊆R^(n)   (25)

x₀=x_(IC)   (26)

x_(N) ∈ T⊆R^(n)   (27)

u_(k) ∈U_(k) ⊆ R^(m)   (28)

w_(k) ∈ W_(k)⊆R¹   (29)

∀k=0, 1, . . . , N-1   (30)

The function g_(N)(x_(N)) is the terminal cost term and the termg_(k)(x_(k),u_(k),ω_(k)) is the stage cost, i.e. the cost associatedwith applying the control action u_(k), at a discrete time (or distance)k to the discrete time dynamic system (Equation 24). The notation forthe functions f_(k), g_(k) indicates that both the cost term and thedynamic system can be time-varying. The initial condition is set tox_(IC) and the state at the last iteration is constrained within the setT. The state variables, control inputs and exogenous inputs areconstrained into time-variant sets X_(k), U_(k), and W_(k),respectively.

Dynamic Programming

The dynamic programming algorithm is an optimization method whichidentifies a global optimal solution given a problem formulation andconstraints. The dynamic programming algorithm is based on what isreferred as Bellman's “Principle of Optimality” to simplify a complexproblem by breaking it down to smaller chunks recursively, withoutsacrificing optimality 25 (Bellman, R., “Dynamic programming,” (CourierCorporation, 2013)). Typically, the dynamic programming algorithm isused to determine the optimal controller which is not causal as toproduce a benchmark for any other causal controller. On the assumptionthat all the future disturbances and reference inputs are known at theonset of computation, the controller 2 could be used in real-timecontrol applications.

For the optimal control problem to be solved numerically, the time (ordistance), the state space, and the control space need to bediscretized. At index k, the state space is discretized to the setX_(k)={x_(k) ¹,x_(k) ², . . . , x^(k) ^(p)}, where the superscriptdenotes the grid point at a given index k, with p indicating the numberof grid points at x index. Similarly, the control space set is definedas U_(k)={u_(k) ¹, . . . , u_(k) ^(p)}. The dynamic programmingalgorithm proceeds backwards in time (or distance) from N-1 to 0 toevaluate the optimal cost-to-go function J_(k)(x^(i)) at every gridpoint in the discretized distance (or time) space:

-   -   1. End cost calculation step:

$\begin{matrix}{{J_{N}\left( x^{i} \right)} = \left\{ \begin{matrix}{{g_{N}\left( x^{i} \right)},{{{for}\mspace{14mu} x^{i}} \in T}} \\{\infty,{else}}\end{matrix} \right.} & (31)\end{matrix}$

-   -   2. Intermediate calculation step:

$\begin{matrix}{{J_{k}\left( x^{i} \right)} = {\begin{matrix}\min \\{u_{k} \in U_{k}}\end{matrix}\left\{ {{g_{k}\left( {x^{i}.u_{k}} \right)} + {J_{k + 1}\left( {f_{k}\left( {x^{i},u_{k},\omega_{k}} \right)} \right)}} \right\}}} & (32)\end{matrix}$

The control policy π={u₀(x),μ₁(x), . . . , μ_(N-1)(x)} is optimal if itconsists of the optimal control signal at each node which minimizes theright side of this equation. Multilinear interpolation is used toevaluate the cost to go function when the control policy falls betweengrid points.

The communication between the host vehicle 1 and the surroundinginfrastructure and target vehicles 15-n is illustrated in FIG. 3. Thecontroller 2 in the preset embodiment is scalable depending on the levelof information available and is operable when V2V and/or V2Icommunication is unavailable. The controller 2 communicates withinfrastructure, such as the traffic control signals 15-n on the route R.The controller 2 also communicates with one or more target vehicle 15 toassess the traffic surrounding the host vehicle 1, for example thetraffic ahead of the host vehicle 1 on the route R. The controller 2 mayoptionally communicate with a remote server, for example over a wirelesscommunication network, to extend the horizon. The communication with theremote server may identify a road incident on the route R and/or providereal-time traffic information on the route R.

The acceleration of the host vehicle 1 is controlled in response to roadattributes, such as road curvature, changes in altitude, altitude,intersections and traffic control signals; and/or changes in drivingconditions, such as speed limits and traffic/congestion. The controller2 may also be configured to take account of additional factors. Forexample, the selection of a low cruising speed may improve operatingefficiency but result in an unacceptable increase in the journey time.The journey time to energy usage trade-off, is typically nonlinear andwill depend on the specific driving scenario. A schematic representationof the architecture of the controller 2 is shown in FIG. 4. Thefunctions are categorized as: (i) predictive control algorithms; (ii)supporting functions that combine information from various sources; and(iii) vehicle on-board controllers which supply the necessaryinformation. The predictive control algorithms comprise a vehicle speedcontrol unit 20 and a hybrid powertrain control unit 21. The supportingfunctions comprise a route-based predictive optimizer 22, a static speedconstraints calculator 23, an energy recuperation estimator 24, a targetvehicle speed trajectory predictor 25, an auxiliary load estimator 26and a road-load estimator 27. The vehicle on-board controllers comprisea route preview calculator 28, such as an eHorizon module available fromContinental AG; a powertrain control module 29 and a V2I communicationmodule 30. The route-based predictive optimizer 22 is used topre-emptively determine a State of Charge (SOC) of the traction battery6 throughout a journey. The route-based predictive optimizer 22 may, forexample, takes into consideration trip information such as one or moreof the following: road speed limits, historical aggregated vehiclespeed, road gradient, road type and the available energy from thetraction battery 6. The road-load estimator 27 is provided to estimatethe traction torque requirement. The auxiliary load estimator 26 may,for example, predict DC-DC converter and HVAC demand. The energyrecuperation estimator 24 estimates energy recuperation. The hybridpowertrain control unit 21 is configured to constantly adapts the levelof deceleration of the host vehicle 1 in dependence on the determinedSOC and the future potential for energy recuperation.

Static Velocity Limit Determination

With reference to FIG. 5, the static speed constraints calculator 23receives the following signals from the route preview calculator 28 inthe form of a receding horizon:

-   -   A road gradient array θ_(road,vec)=[d_(θ) _(road,hor)        θ_(road,hor)] comprising the road grade angle vector        θ_(road,hor) at the corresponding distance vector d_(θ)        _(road,hor) .    -   A road curvature array [d_(φ) _(road,hor) φ_(road,hor)]        comprising the road curvature angle vector θ_(road,hor) at the        corresponding distance vector φ_(road,hor).    -   A speed limit array [θ_(v) _(lim,hor) V_(lim,hor)] comprising        the road speed limit vector V_(lim, hor) at the corresponding        distance vector d_(v) _(lim,hor) .

The static speed constraints calculator 23 comprises a maximum speedroad curvature module 31, a maximum speed limit arbitration module 32, alongitudinal acceleration look-up module 33, a lateral accelerationlook-up module 34 and a speed constraint smoothing module 35. The speedconstraint smoothing module 35 receives the outputs from the routepreview calculator 28, the speed limit arbitration module 32, thelongitudinal acceleration look-up module 33 and the lateral accelerationlook-up module 34 and generates maximum and minimum speed constraintsV_(lim,max,hor), V_(lim,min,hor). The speed constraint smoothing module35 outputs the following arrays:

-   -   A minimum speed array [d_(V) _(lim,min,hor) V_(lim,min,hor)]        comprising the minimum speed constraint V_(lim,min,hor) at the        corresponding distance vector d_(V) _(lim,min,hor) .    -   A maximum speed array [d_(V lim,max,hor) V_(lim,max,hor)]        comprising the maximum speed constraint V_(lim,max,hor) at the        corresponding distance vector d_(V) _(lim,max,hor) .

The maximum speed road curvature module 31 calculates a speed limit dueto lateral acceleration exerted on the host vehicle 1 when travellingaround a bend in a road (the curvature of the bend being determined withreference to geographical map data). The maximum speed constraint isidentified as the smaller of the speed determined by the maximum speedlimit arbitration module 32 and the maximum speed road curvature module31. Subsequently, the speed constraint smoothing module 35 smooths themaximum speed limit according to lateral and longitudinal accelerationtarget look-up tables defined by the longitudinal and lateralacceleration look-up modules 33, 34. The smoothing module may alsoconsider the road gradient. The minimum speed constraint may be derivedas a percentage of the equivalent maximum speed constraint, but alsoconsidering the actual vehicle speed (so that optimization is notconstrained into an infeasible region). Alternatively, or in addition,functional road class or road type can also be considered in thedetermination of the lowest speed. As shown in FIG. 4, the minimum speedarray [d_(V) _(lim,min,hor) V_(lim,min,hor)] and the maximum speed array[d_(V) _(lim,max,hor) V_(lim,max,hor)] are output to the vehicle speedcontrol unit 20.

Leading Vehicle Velocity Trajectory Prediction

The target vehicle speed trajectory predictor 25 is configured topredict the speed of any target vehicles 15-n in the vicinity of thehost vehicle 1, particularly any target vehicles 15-n which may hinderor obstruct the motion of the host vehicle 1 along the route R. Thecurrent state of the target vehicles 15-n is transmitted to the hostvehicle 1 as part of the V2V communication. Typical informationavailable from the V2V communication includes the current speed,acceleration and location of the target vehicle 15-n. A rule-based modelfor predicting the speed of a target vehicle 15-n is illustrated in FIG.6. The prediction is conducted for each target vehicle 15-n, one targetvehicle 15-n at a time, within an optimization horizon of the hostvehicle 1 along the route R. The optimization horizon may consist of asub-section of the route R, the optimization horizon continuallychanging as the host vehicle 1 progresses along the route R (providing arolling horizon). The optimization horizon may, for example, comprise asub-section of the route R having a length greater than or equal to 250m, 500 m, 750, or 1,000 m. Alternatively, the optimization horizon mayconsist of the entire route R. The algorithm starts with the targetvehicle 15-n the furthest away from the host vehicle 1 and progresseswith target vehicle 15-n closer to the host vehicle 1. The prediction ofthe speed of each target vehicle 15-n assumes that an initial rate ofacceleration or deceleration continues for a predetermined period oftime.

A model for predicting the speed of a first target vehicle 15-1 is shownin FIG. 6. The model is initiated (BLOCK 100). In the case of an initialdeceleration, the prediction assumes the first target vehicle 15-1 willcontinue to decelerate at a constant rate of deceleration for apredetermined period of time (BLOCK 105). The predetermined period oftime for deceleration of the first target vehicle 15-1 is calibratable.A more accurate prediction may be achieved by assuming that thedeceleration will end after a few seconds, rather than assuming that thevehicle will continue to decelerate until it comes to a standstill.After an initial period of deceleration, the first target vehicle 15-1may be assumed to start accelerating again. If the first target vehicle15-1 is determined to have stopped, an assumption is made that it willremain stationary for a predetermined period of time and will thenaccelerate at a predetermined acceleration. The period of time that thefirst target vehicle 15-1 remains stationary is calibratable, as too isthe acceleration. In the case of an initial acceleration, the predictionassumes that the first target vehicle 15-1 will continue to acceleratefor a predetermined period of time (BLOCK 110). The predetermined periodof time for acceleration of the first target vehicle 15-1 iscalibratable. The controller 2 may change the predicted movement of thehost vehicle 1 in response to a change in the environment. For example,the prediction model would transition from assuming the continuedacceleration of the first target vehicle 15-1 if the first targetvehicle 15-1 is identified as following a second target vehicle 15-2,i.e. a preceding vehicle (BLOCK 115). This change may, for example, beimplemented upon determining that the first target vehicle 15-1 iswithin a predefined distance of the second target vehicle 15-2. Theprediction model assumes that the first target vehicle 15-1 willsubsequently attempt to keep a certain headway between the first targetvehicle 15-1 and the second target vehicle 15-2. The model may define atarget headway distance between the first target vehicle 15-1 and thesecond target vehicle 15-2. Another possibility is that the initialacceleration or deceleration results in the speed of the first targetvehicle 15-1 being substantially equal to a determined speed limit(either a legal speed limit or a speed limit determined by roadcurvature) in which case the prediction would assume that the firsttarget vehicle 15-1 would proceed at the speed limit (BLOCK 120). If thefirst target vehicle 15-1 gets close to the second target vehicle 15-2,the predicted speed of the first target vehicle 15-1 is reduced. Notethat there is no possible transition from the first target vehicle 15-1following the second target vehicle 15-2 to following the speed limits.This is because the prediction would never predict any of the targetvehicles 15-n as exceeding the speed limit (at least for longer thanmomentarily e.g. when speed limit is decreasing), nor would it try topredict any overtaking. Consequently, a large gap between the firsttarget vehicle 15-1 and the second target vehicle 15-2 cannot developand thus this transition is not necessary. The prediction model could bemodified also to take into account infrastructure, for example trafficcontrol signals. It will be understood that the prediction model may beupdated cyclically when new information is available regarding theposition and/or movements of the target vehicles 15-n. The predictionmodel predicts the speed and movement of each of the identified targetvehicles 15-n. Other techniques for modelling the speed and movement ofthe target vehicles 15-n may be used.

Optimization Algorithm Formulation

Problem Formulation and Decomposition

The determination of an appropriate vehicle speed trajectory and thecontrol of the vehicle propulsion system is dependent on a plurality ofstates/inputs and time-variant, nonlinear system dynamics. Thecontroller 2 utilises the following states and inputs:

State: x=[t V _(veh) SOC κ_(gr)]  (33)

Control input: u=[a _(veh) u ₁ u ₂ u ₃ ]   (34)

Ex. input: ω_(k) =[E _(dcdc,est)θ_(road,vec) T _(ice) T _(HV) c _(F)_(rl) ]   (35)

where t,E_(dcdc,est), T_(ice), T_(HV), and c_(F) _(rl) denote time, anestimate of auxiliary energy consumption, ICE coolant temperature, HVbattery temperature and the road-load force coefficients (at zero roadgradient), respectively within the optimization horizon. The front axletransmission input u₃ is defined as:

$\begin{matrix}{u_{3} = \left\{ \begin{matrix}{1,} & {{gear}\mspace{14mu} {upshift}} \\{0,} & {{gear}\mspace{14mu} {hold}} \\{{- 1},} & {{gear}\mspace{14mu} {downshift}}\end{matrix} \right.} & (36)\end{matrix}$

A level of approximation is appropriate. One option would be tolinearize the system (as defined in Equation 24) and make variousapproximations to the constraints (as defined in Equations 25 to 29).This option is not implemented in the present embodiment. An alternativewould be to sacrifice a level of optimality, using an approximateNonlinear Model Predictive Controller algorithm (NMPC). As outlinedabove, the dynamic programming algorithm has been implemented in thepresent embodiment. In order to reduce the computational burden of thedynamic programming algorithm, the optimization problem is decomposedinto two stages, as represented by the vehicle speed control unit 20 andthe hybrid powertrain control unit 21 in FIG. 4. The vehicle speedcontrol unit 20 and the hybrid powertrain control unit 21 will now bedescribed in more detail.

Vehicle Speed Optimization

The vehicle speed control unit 20 receives the following:

-   -   Static speed constraints from function: Static Speed Constraints        Calculation.    -   Time-varying speed constraints from function: Surrounding        Vehicle Speed Trajectory Predictor.    -   Time-repeatable speed constraints from the V2I communication        channel. This includes the green and red phasing of the traffic        control signals.    -   The current vehicle speed (as initial condition) and SOC.    -   The array θ_(road,vec) and the road-load force coefficients        c_(F) _(rl) .

Setting aside the time variant derived from the V2X communication, thedynamic programming problem cost can be defined as follows:

g _(k)(x _(k) ,u _(k), ω_(k))=W _(time) t+W _(acc) a _(veh) ² +W _(road)F _(road)   (37)

with

State: x_(k=V) _(veh)   (38)

Control input: u_(k)=a_(veh)   (39)

Exogenous input: 107 _(k)=[θ_(road,vec) c _(F) _(rl) ]   (40)

where W_(time), W_(acc), and W_(road) are the cost weights for time termt, the square acceleration term a_(veh) ², and the road-load force termF_(road)=F_(r)+F_(a)+F_(g), respectively. A distance-based grid isadopted. The W_(time), W_(acc), W_(road) reflect the relative importanceof each term. The acceleration term is used to avoid aggressive(de)accelerations. W_(acc) could be a function of SOC, i.e. W_(acc)=f(SOC) and predicted recuperation energy, to adapt the level ofacceleration or deceleration according to the powertrain state. The timeterm is used to discourage input mode transitions which add significanttime to the journey. Finally, the road-load term discourages excessivelyhigh vehicle cruising, as aerodynamic losses exponentially increase withvehicle speed. The time during a mode transition is calculated startingfrom the following equations:

½a _(veh,D) _(s) t _(D) _(s) ² +v _(start,D) _(s) t _(D) _(s) =D _(s)  (41)

v _(start,D) _(s) =v _(end,D) _(s) −a _(veh,D) _(s) t _(D) _(s)   (42)

where a_(veh,D) _(s) is acceleration used during distance step D_(s),t_(D) _(s) is the time spent to cover distance step D_(s), v_(start,D)_(s) is the vehicle speed at the beginning of the distance step, andv_(end,D) _(s) the vehicle speed at the end of the distance step.

The vehicle speed at the end of the distance step v_(end,D) _(s) and theacceleration during the distance step a_(veh,D) _(s) are known based onthe model inputs. The distance step D_(s) is also known based on theoptimization problem definition. The vehicle speed at the beginning ofthe distance step v_(start,D) _(s) (model output state in forwarddynamic programming) and the time to cover the distance step t_(D) _(s)can be calculated. The time spent to cover the distance step t_(D) _(s)is required for time-keeping and cost calculation. The vehicle speed atthe beginning of the distance step v_(start,D) _(s) is obtained directlyfrom Equation (42); and the time to cover the distance step t_(D) _(s)can be obtained by substituting Equation (42) into Equation (41). Thisresults in the following second order polynomial equation:

−½a _(veh,D) _(s) t _(D) _(s) ² +v _(end,t) _(Ds) t _(D) _(s) −D _(s)=0  (43)

The solution of this quadratic equation is given by:

$\begin{matrix}{t_{D_{s}} = \frac{v_{{end},D_{s}} \pm \sqrt{v_{{end},D_{s}}^{2} - {2a_{{veh},D_{s}}D_{s}}}}{a_{{veh},D_{s}}}} & (44)\end{matrix}$

From the two resulting roots of the equation, the smaller positivenon-complex root is selected.

The V2X speed optimization constraints, such as the target vehicles15-n, the traffic control signals 18-n and other traffic objects, aretime-dependent obstacle. A comparison of the static vehicle speedconstraint against the speed constraint due to a traffic control signalis represented in a two-dimensional (2D) optimization grid 40 shown inFIG. 7A; and a corresponding three-dimensional (3D) optimization grid 41shown in FIG. 7B. The two-dimensional (2D) optimization grid 40 consistsof a two-dimensional speed against distance map. The three-dimensional(3D) optimization grid 41 consists of a three-dimensional speed,distance and time map. In the illustrated example, a traffic controlsignals 18-n are located at a position d_(k)=400 m, ahead of a currentvehicle position d₀=0 m.

The traffic control signals 18-n impose a speed constraint during a redphase when the progress of the host vehicle 1 would be impeded. Thetraffic control signals 18-n do not impose a speed constraint during agreen phase when the progress of the host vehicle 1 would be at leastsubstantially unhindered. The operating state of the traffic controlsignals 18-n is represented in the 3D optimization grid 41 by a squarewave 42 having a non-zero value during the red phase and a zero valueduring the green phase. In the illustrated arrangement, the red phase ofthe traffic control signals 18-n has a duration of 20 to 40 seconds. Astatic speed constraint due to road topology/speed limits is representedby a first continuous line 43 in the 2D optimization grid 40, and by acontinuous surface 44 within the 3D optimization grid 41. The hostvehicle 1 is travelling with an initial speed V_(veh,0)=100 km/h. Thegrid points X₀, X_(k-1), X_(k), and X_(N) represent analysis planes atdistance d₀=0 m, d_(k-1), d_(k), and d_(N)=500 m, respectively. In the2D optimization grid 40, potential first and second trajectories 45, 46from point A to point B are shown. The first and second speedtrajectories 45, 46 are also shown in the 3-D optimization grid 41. Thefirst and second speed trajectories 45, 46 end at points B₁, B₂respectively in the 3-D optimization grid 41. The first trajectory 45 isvalid since it results in the host vehicle 1 traversing the location ofthe traffic control signals 18-n during a green phase. The secondtrajectory 46 is invalid since it results in the host vehicle 1traversing the location of the traffic control signals 18-n during a redphase. Thus, only the first trajectory 45 (extending from A to B₂) isfeasible with regards to traffic control signal constraints.

If the analysis is performed within a 2-D plane, the time-varying speedconstraints would only be considered during the transition from X_(k-1),to X_(k) in a forward dynamic programming optimization. Considering thetime-varying speed constraint at d_(k), the already calculated optimizedtrajectories, from any grid point of X₀ to X_(k-1) in the 2-Doptimization grid 40 may no longer be optimal, or may be infeasibleduring the transition from X_(k-1) to X_(k). To overcome this problem,the optimization space could be increased also to include time as anoptimization state. However, this exponentially increases the possibletransitions from grid plane X₀ to X_(k) and significantly increasescomputational burden.

An alternative problem formulation may utilise an approximation thatavoids the need to add time as an optimization state. A separate costfunction is added to the dynamic programming algorithm to penalizecontrol actions that are likely to have undesired time trajectories. Alevel of optimality is potentially sacrificed using this approach, butit is believed that any such loss is acceptable, for example compared touncertainty arising from traffic flow predictions. Conversely, theproposed solution further discourages frequent fluctuations in vehiclespeed that may otherwise have been selected. By way of example, costconsiderations can be added for traffic control signals 18-n and targetvehicles 15-n. The dynamic programming algorithm is calculated forwards,i.e. from the current time at the beginning of algorithm execution, todetermine whether or not time-variant constraints, such as the trafficcontrol signal 18-n, will be violated (i.e. whether or not one or moretraffic control signal 18-n on the route R will impede progress of thehost vehicle 1).

The operation of the controller 2 will now be described in relation to ascenario illustrated in FIG. 8 in which the host vehicle 1 isapproaching a first traffic control signal 18-1. A two-dimensionaloptimization grid 50 is generated consisting of a two dimensional speedagainst distance map. A first traffic control signal 18-n is identifiedat a first location k on the route R. First and second accelerationlimits for the host vehicle 1 are calculated to arrive at the firstlocation K during a time period corresponding to a green phase of thefirst traffic control signal 18-1 (represented by a double-headed arrowl in FIG. 8). The first acceleration limit a_(OV) corresponds to thehost vehicle 1 arriving at the first traffic control signal 18-1concurrent with the beginning of the green phase l, i.e. as the firsttraffic control signal 18-1 turns green (a_(TL) ^(l,green)). The firstacceleration limit a_(TL) corresponds to a constant acceleration ordeceleration that would cause the host vehicle 1 to arrive at the firstlocation K at a first arrival time corresponding to a time when thefirst traffic control signal 18-1 enters a first green phase. The secondacceleration limit corresponds to the host vehicle 1 arriving at thefirst traffic control signal 18-1 contemporaneous with the end of thegreen phase l, i.e. as the first traffic control signal 18-1 turns red(a_(TL) ^(l,red)). The second acceleration limit a_(TL) corresponds to aconstant acceleration or deceleration that would cause the host vehicle1 to arrive at the first location K at a second arrival timecorresponding to a time when the first traffic control signal 18-1 exitsthe first green phase. The first and second acceleration limits a_(TL)are calculated for the host vehicle 1 in respect of each grid point inthe 2-D optimization grid 50 between the current position of the hostvehicle 1 and the traffic control signal 18-n. In the exampleillustrated in FIG. 8, the first and second acceleration limits a_(TL)are calculated at the grid points x₀ ⁴(corresponding to point A) andgrid point x₁₄ ³; the first and second speed trajectories 51, 52 foreach these grid points is illustrated. The first and second accelerationlimits define upper and lower speed trajectories 51, 52 for the hostvehicle 1. The upper and lower speed trajectories 51, 52 define a targetoperational speed band 53. A cost is applied for any accelerationtransitions that violate the first and second acceleration limits (i.e.a cost is applied if the actual acceleration of the host vehicle 1 isoutside the range defined by the first and second acceleration limits).Consequently, the traffic control signal cost could prompt the dynamicprogramming algorithm to favour lower speed trajectories, for examplewhen a higher speed trajectory will result in the host vehicle 1arriving at the first traffic control signal 18-1 during a red phasewhich would necessitate the host vehicle 1 stopping. It will beappreciated that the operation of the first traffic control signal 18-1is cyclical and the green and red phases alternate, thereby providing aplurality of opportunities for the host vehicle 1 to pass the firsttraffic control signal 18-1 during a green phase. By way of example,first and second green phases l1, l2 are shown in the two-dimensionaloptimization grid 50. The first and second acceleration limits a_(TL)may be calculated for a plurality of red phases and/or green phases.

The calculation of the acceleration limit a_(TL) will now be describedby way of example. The speed, distance and time are known for a gridpoint A. At a grid point C corresponding to the traffic control signal18-1 transitioning to the green phase, the distance and time are known,but the speed of the host vehicle 1 is not known. By way of example, atthe grid point A the first speed (Sp1) of the host vehicle 1 is 100 kph(27.8 m/s), the first distance (d1) is zero (0) metres and the firsttime (time1) is zero (0). At the grid point C, the second speed (Sp2) ofthe host vehicle 1 is unknown, the second distance (d2) is 400 metresand the second time (time2) is 20 seconds. The following kinematicequations can be used to determine the acceleration limit a_(TL) and thesecond speed (Sp2):

Sp2=SP1+alim×(time2-time1)

d2-d1=(time2-time1)*(Sp2+Sp1)/2

One of the equations is solved for one unknown (either the accelerationlimit a_(TL) or the second speed (Sp2)) and the result substituted inthe other equation.

In the arrangement illustrated in FIG. 8, a lower static optimisationlimit is set (20 kph in the present example), but this is not essential.As the host vehicle 1 moves forward along the route R, the cost functionis evaluated for each possible acceleration action. Each action isassociated with a time interval (see equation 44). By adding the timeinterval for a given speed trajectory, the processor 12 determineswhether each speed trajectory will result in the host vehicle 1 passingthrough the traffic control signal 18-1 during a green phase or a redphase. If the speed trajectory remains within the operational speed band53 defined by the upper and lower speed trajectories 51, 52, the hostvehicle 1 will pass through the traffic control signal 18-1 during agreen phase.

It will be understood that there may be a single traffic control signals18-n on the route R, or there may be a plurality of traffic controlsignals 18-n on the route R. The following control strategy is used todetermine the cost related to the one or more traffic control signal18-n located within the optimization horizon on the route R:

-   -   1. For each traffic control signal 18-n within the optimization        horizon and its each green phase compute a_(TL) ^(l,green) and        a_(TL) ^(l,red).    -   2. For each transition that does not fall within a green phase,        compute violation to closest limit a_(viol)=|a_(veh)-a_(TL)        ^(lim)|.    -   3. Add cost to these violating transitions

$g_{TL} = {\frac{a_{viol}{WTL}_{1}}{a_{{rem},{TL}}^{{WTL}_{2}}\left( {1 + {M_{TL}{WTL}_{3}}} \right)}.}$

The cost function g_(TL) increases the associated cost as the violationa_(viol) increases, the cost decreases as the distance remaining to thetraffic control signal d_(rem,TL) increases and as the number of trafficcontrol signals between the currently considered traffic control signaland the host vehicle 1 M_(TL) increases. The weightings of thesedifferent considerations can be tuned with the following coefficients:WTL₁ ∈(0, ∞), WTL₂ ∈ [0, ∞) and WTL₃ ∈ [0, ∞). At least in certainembodiments, the cost related to each traffic control signal 18-ndecreases as the distance between the host vehicle 1 and the trafficcontrol signal 18-n increases.

A similar cost function can be applied with regards a target vehicle15-n, for example to calculate a target speed trajectory band for thehost vehicle that avoids approaching a target vehicle 15-n in front ofthe host vehicle 1 with a large speed difference. The progress of thetarget vehicle 15-n along the route R is predicted, for exampleutilising the model described herein with reference to FIG. 6. Theapplication of a suitable cost generates a speed profile that results inthe host vehicle 1 gradually reducing speed to maintain a target headwaybetween the host vehicle and the target vehicle 15-n. At least incertain embodiments, a gradual approach to the target vehicle 15-n maybe more energy efficient as it allows increased coasting and mitigatesthe need to use friction brakes. This can be done by first making aprediction of the speed of the target vehicle(s) 15-n within theoptimization horizon. This prediction is used in a cost function tocompute how each transition would affect the headway between the hostvehicle 1 and the target vehicle 15-n. The target vehicle 15-n isidentified at a first location K and the speed of the target vehicle15-n determined at the first location K. The target vehicle 15-n in thepresent embodiment is assumed to be travelling at a constant speed forthe purposes of predicting its movement along the route R. A firstacceleration limit a_(OV) is calculated for the host vehicle 1. It willbe understood that other techniques may be implemented to model movementof the target vehicle 15-n, for example comprisingacceleration/deceleration and/or local infrastructure, such as trafficcontrol signals. The first acceleration limit a_(OV) defines a constantacceleration or deceleration for the host vehicle 1 which will result inthe host vehicle 1 arriving at the first location K at a first arrivaltime with a vehicle speed which is substantially equal to or less thanthe speed of the target vehicle 15-n at the first location K. The firstarrival time is selected to provide a target headway between the hostvehicle 1 and the target vehicle 15-n when the host vehicle 1 arrives atthe first location K. The first acceleration limit is calculated for thehost vehicle 1 in respect of each grid point in a 2-D optimization grid.The acceleration limit is used to determine a target operational speedband for the host vehicle 1. If the first acceleration limit is violated(i.e. the actual acceleration of the host vehicle 1 differs from thefirst acceleration limit), a cost is applied to the optimized speedprofile. In the present embodiment, if the deceleration of the hostvehicle 1 is less than the acceleration limit a_(OV), a cost is appliedas the host vehicle 1 will arrive at the first location K with a higherspeed than that of the target vehicle 15-n). If the acceleration of thehost vehicle 1 is greater than or equal to the acceleration limita_(OV), no cost is applied as the host vehicle 1 will approach thetarget vehicle 15-n gradually with a smaller speed differential, therebyreducing or avoiding harsh or reactive deceleration.

A control strategy to determine the cost related to the target vehicle15-n (referred to herein as the target vehicle cost g_(OV)) is asfollows:

-   -   1. Compute an acceleration a_(OV) and distance vector        d_(rem,hw,min) for the target vehicle 15-n.    -   2. For each transition, compute violation of the acceleration        limit a_(viol)=|a_(veh)-a_(OV)|.    -   3. Add target vehicle cost g_(OV)=0 to each violating        transition:

$g_{ov} = {\left( {1 - \frac{a_{{rem},{hw},{mi}}}{a_{{hw},{pe},\max}}} \right){WOV}_{1}{a_{viol}.}}$

-   -   4. Set the target vehicle cost g_(OV)=0 when distance to minimum        headway is large: d_(rem,hw,min)>d_(hw,pen,max) or if        a_(veh)<a_(OV).

In this scenario, the target vehicle cost g_(OV) is the cost associatedwith the target vehicle 15-n, d_(rem,hw,min) is the distance from theminimum headway to the other vehicle, d_(hw,pen,max) is the distancebeyond which no penalties related to the target vehicle 15-n areapplied, and WOV₁ ∈ [0, ∞) is a penalty coefficient determining theoverall importance of the target vehicle cost g_(OV). The target vehiclecost g_(OV) decreases as the distance between the host vehicle 1 and thetarget vehicle 15-n increases.

The overall speed optimization cost function g_(k)(x_(k),u_(k),ω_(k))can now be augmented with the traffic control signal costg_(nand the target vehicle cost g) _(OV):

g _(k)(x _(k),u _(k),ω_(k))=W _(time) t+W _(acc) a _(veh) ² +W _(road) F_(road) +g _(TL) +g _(OV)   (45)

The operation of the controller 2 will now be described in relation tofirst lead vehicle scenario illustrated in FIG. 9. The host vehicle 1 isapproaching from behind a first target vehicle 15-1 which is travellingalong the route R. A two-dimensional optimization grid 60 is generatedconsisting of a two dimensional speed against distance map. Thetwo-dimensional optimization grid 60 relates a distance from the hostvehicle 1 along the route R to the speed of the host vehicle 1. Thefirst target vehicle 15-1 is identified at a first location

K on the route R. The progress of the first target vehicle 15-1 alongthe route R is predicted assuming at a constant speed (for exampledetermined via V2V communication or using on-board sensors on the hostvehicle 1). A first acceleration limit a_(OV) is calculated for the hostvehicle 1 to determine a first speed trajectory 61 for controlling thehost vehicle 1 to arrive at the first location K at a speed which isless than or equal to the determined speed of the first target vehicle15-1. The first acceleration limit a_(OV) corresponds to a constantacceleration or deceleration that would cause the host vehicle 1 toarrive at the first location K at a first arrival time with a vehiclespeed which is substantially equal to or less than the speed of thetarget vehicle 15-n at the first location K. The first arrival time isselected to provide a target headway 62 between the host vehicle 1 andthe target vehicle 15-n when the host vehicle 1 arrives at the firstlocation K. In the arrangement illustrated in FIG. 9, this isimplemented by calculating the first acceleration limita_(OV for a position which is offset relative to the first location K y a distance corresponding to a target headway 62. The first acceleration limit a)_(OV) is calculated at each grid point in the two-dimensionaloptimization grid 60. A cost is applied based on a deviation of theactual acceleration of the host vehicle 1 from the acceleration limita_(OV). The cost is determined in dependence on the magnitude of thedeviation. An acceleration of the host vehicle 1 which is greater thanthe acceleration limit a_(OV) is penalised. The distance vectord_(rem,hw,min) directly affects the cost. By way of example, the initialspeed of the host vehicle 1 may be 50 km/h and the first target vehicle15-1 may have a constant speed of 20 km/h. At the starting position, theacceleration limit a_(OV) corresponds to a constant deceleration thatwould cause the host vehicle 1 to slow down from 50 km/h to 20 km/hwhile moving to the initial position of the first target vehicle 15-1.As illustrated in FIG. 9, the headway 62 is maintained between the hostvehicle 1 and the first target vehicle 15-1 as a safety consideration.As speeds of the host vehicle 1 and the first target vehicle 15-1 are atleast substantially equal to each other, the headway 62 remainsconstant. In order to avoid an unnecessarily large headway 62, a smallviolation of the acceleration limit a_(OV) may be permitted. Thus, nocost may be applied for a deceleration of the host vehicle 1 which islower than the acceleration limit a_(OV) within a predetermined margin,for example expressed as a proportion of the acceleration limit a_(OV).The dynamic programming algorithm may flag any trajectory as infeasiblewhich would result in the host vehicle 1 getting closer to the firsttarget vehicle 15-1 than a predetermined minimum headway. In thisexample, the first speed trajectory 61 defines an upper limit of atarget operational speed trajectory band 63. The operational speedtrajectory band 63 is the area below the first speed trajectory 61 shownin FIG. 9. Other static constraints could be applied to reduce thetarget speed trajectory band.

The first target vehicle 15-1 may hinder or impede progress of the hostvehicle 1 depending on the location on the route R where the hostvehicle 1 encounters the first target vehicle 15-1. For example, thehost vehicle 1 may be hindered if the first target vehicle 15-1 isencountered on a section of road which is favourable forperformingunfavourable for performing an overtaking manoeuvre, forexample a section of road having a single lane or where overtaking isnot permitted. Conversely, the host vehicle 1 may continue substantiallyunhindered if the first target vehicle 15-1 is encountered on a sectionof road which is favourable for performing an overtaking manoeuvre, forexample a section of road or highway having multiple lanes. Theoperation of the controller 2 will now be described in relation tosecond lead vehicle scenario illustrated in FIG. 10. The controller 2 isconfigured to identify an overtaking opportunity 64, for examplecorresponding to a section of the route R favourable for performing anovertaking manoeuvre. As illustrated in FIG. 10, the overtakingopportunity 64 may be defined in the two-dimensional optimization grid60 as extending over a predetermined distance relative to the currentlocation of the host vehicle 1. The overtaking opportunity 64 isidentified as extending between a first location K1 and a secondlocation K2 (represented in the two-dimensional optimization grid 60 asrespective first and second distances relative to the current locationof the host vehicle 1). A first acceleration limit a_(OV) is used todetermine a first speed trajectory 65 to control the host vehicle 1 toarrive at the first location K1 at a first arrival time which is thesame as or later than the time that the first target vehicle 15-1 willarrive at the first location K1. A second acceleration limit a_(OV) isused to determine a second speed trajectory 66 to control the hostvehicle 1 to arrive at the second location K2 at a second arrival timewhich is the same as or before the time that the first target vehicle15-1 will arrive at the second location K2. The first and secondacceleration limit a_(OV) define a constant acceleration or decelerationfor the host vehicle 1. The first and second acceleration limits a_(OV)are calculated at each grid point in the two-dimensional optimizationgrid 60. The first and second speed trajectories 65, 66 define a targetoperational speed band 67 for the host vehicle 1. As shown in FIG. 10,the target operational speed band 67 is bounded by the first and secondspeed trajectories 65, 66. A cost is applied for any accelerationtransitions that violate the first and second acceleration limitsa_(OV). The traffic control signal cost could prompt the dynamicprogramming algorithm to apply a bias in favour of a lower speedtrajectory, for example when a higher speed trajectory will result inthe host vehicle 1 approaching the first target vehicle 15-1 before theidentified overtaking opportunity 64. Conversely, the traffic controlsignal cost could prompt the dynamic programming algorithm to apply abias in favour of a higher speed trajectory, for example when a lowerspeed trajectory will result in the host vehicle 1 approaching the firsttarget vehicle 15-1 after the identified overtaking opportunity 64. Theprocessor 12 determines that the target vehicle 15-1 is not relevant ifthe overtake opportunity is taken, but continues to monitor the targetvehicle 15-1 if the overtaking opportunity is missed.

Rather than an overtaking opportunity 64, the route R may comprise anintersection and the processor 12 may determine that the host vehicle 1will encounter the first target vehicle 15-1 at the intersection. Again,the time that the host vehicle 1 arrives at and/or exits theintersection may determine whether progress is hindered by the firsttarget vehicle 15-1.

Hybrid Powertrain Optimization

The operation of the hybrid powertrain control unit 21 will now bedescribed. The hybrid powertrain control unit 21 receives:

-   -   The array [d_(V) _(veh,opt,hor) V_(veh,opt,hor)] which contains        optimized vehicle trajectory V_(veh,opt,hor) at the        corresponding distance vector d_(V) _(veh,opt,hor) .    -   The array θ_(road,vec), the road-load force coefficients c_(F)        _(rl) , and an estimate of auxiliary consumer energy        E_(dcdc,est), in order to account for them in the optimization.    -   The current SOC of the traction battery 6 to set the        optimization initial condition.    -   The array [d_(SOC) SOC_(target)] which contains the SOC target        SOC_(target) at the corresponding distance vector d_(SOC).

The cost function for the powertrain hybrid optimization is set as:

g _(k)(x _(k) ,u _(k) ,ω _(k))=W _(f) {dot over (m)} _(f) +W_(SOC)|SOC_(trgt)−SOC|+W _(u) ₃ |u ₃ |   (46)

with

State: x _(k)=[SOC κ_(gr)]^(T)   (47)

Control input: u _(k) =[u ₁ u ₂ u ₃]^(T)   (48)

Ex. input: ω_(k) =[E _(dcdc,est) θ_(road,vec) T _(ice) T _(HV) c _(F)_(rl) ]   (49)

where W_(f), W_(SOC), and W_(u) ₃ are the cost weights associated withthe fuel economy, SOC and gear cost terms. The SOC term is introduced toensure the SOC is sustained, and for more flexibility could be adaptableto SOC and SOC_(trgt), i.e. W_(SOC)=f_(soc)(SOC,SOC_(trgt)). SOC_(trgt)is provided by the route-based predictive optimizer. The gear cost termW_(u) ₃ is applied to discourage frequent gear shifts.

The vehicle speed control unit 20 determines the target operationalspeed band 67 in dependence on the upper and lower speed trajectories65, 66. The target operational speed band 67 is output from the vehiclespeed control unit 20 as a first output signal SOUT1 to a Vehicle MotionController (VMC) 36 (shown in FIG. 2) responsible for the trajectoryplanning and control of the host vehicle 1. The VMC 36 arbitratesbetween various trajectories and compensates for any speed deviationsfrom the target trajectory. The VMC 36 generates a propulsion torquerequest suitable for maintaining the host vehicle 1 within the targetoperational speed band 67. The propulsion torque request is output bythe VMC 36 as a second output signal SOUT2 to a Vehicle SupervisoryController (VSC) 37. The VSC 37 is configured to intervene to ensuresafety, for example if it determines that operating within the targetoperational speed band 67 could result in a collision, a speed limitviolation or a traffic light violation. A closed-loop controller in theVSC 37 is used to correct for any discrepancies in the demanded torquerequest.

At least in certain embodiments, the techniques described herein forgenerating a target operational speed band offer particular advantages,including improved energy efficiency. One reason is the reduced numberof times that the host vehicle 1 is required to stop, for example at thetraffic control signals 18-n. The host vehicle 1 described herein hasPHEV architecture which is capable of high power energy regenerationduring a braking phase; however, anticipating a stopping event andstarting to decelerate the host vehicle 1 earlier is more efficient, forexample the engine 3 could be disengaged and stopped. It is also to benoted, that there is a two-path efficiency loss(motor/inverter/transmission/traction battery), from regenerating andthen re-using the energy at a later stage. The techniques may offerlarger benefits on vehicles having only an ICE, or a Mild HybridElectric Vehicle (MHEV), where there is no or limited regenerationcapability. Furthermore, the requirement to decelerate the host vehicle1 may be anticipated sooner, even when it is deemed appropriate the hostvehicle 1.

The vehicle speed control unit 20 provides additional benefit as it isbetter able to adapt the powertrain control strategy anticipativelybased on the expected speed profile rather than only knowledge of thecurrent instantaneous vehicle speed. For example, if the targetoperational speed band contains a deceleration, then the powertrainstrategy may for example turn the engine off early because it isdetermined in advance that the host vehicle 1 will start deceleratingand that no propulsive torque is needed from the ICE 3. The increaseduse of the ERAD as the sole source of propulsion torque (i.e. operatingas an EV), also facilitates mild charging of the traction battery 6, forexample at low driver torque demands which shifts the engine torque to amore efficient point.

Dynamic programming is chosen as the optimisation method describedherein due to the optimality of its results and its flexibility to beable to handle challenging non-linear problems such as the oneconsidered here. Typically the computational effort required to performdynamic programming is high, in particular when the number of modelstates and control inputs increase. The technique(s) described hereinreduce model dimensionality, thereby reducing the amount of modelevaluations required to optimise the target speed trajectories, as wellas concentrating the optimization grid points to areas where accuracy ismost needed. Further reductions in computational burden may be achievedby decoupling the speed optimisation from the powertrain usageoptimisation. This modular approach may facilitate application of thetechniques described herein across different vehicle architectures,including conventional vehicles, different hybrid architectures andelectric vehicles. The speed optimisation stage is mostly independent ofpowertrain usage decisions, and only includes high-level vehicleparameters such as mass. Its main optimisation goals are minimizing triptime, anticipating road events ahead (such as traffic lights) whileconsidering traffic rules such as speed limits as well as drivabilityconstraints such as acceleration limits. The powertrain optimizationstage contains a much more detailed model of the specific vehiclearchitecture and is responsible for deciding the relevant controldecisions for that architecture so that the optimized speed profile isfollowed. For example, for a typical parallel hybrid the controldecisions may be the torque split between the engine and the electricmachine, as well as the gear selection. While the speed and powertrainoptimisation procedures are mostly decoupled, some considerations aboutthe powertrain can still be taken in the speed optimisation of the firststage. For example, depending on the current SOC level the algorithmcost function weights may be adapted to encourage certain types of speedprofiles, for instance to increase SOC charging opportunities.

The optimisation algorithm described herein combines inputs including:traffic control timing, behaviour of other vehicles, drivabilityconsiderations as well as road profile and traffic signage. Theinformation originates from a variety of sources which may include V2Icommunication with traffic lights and other infrastructure, V2Vcommunication with other vehicles, communication with an e-Horizondigital map database and in-vehicle sensors. In addition, theoptimisation algorithm may consider a driver identification algorithm toimprove ability to predict actions of the host vehicle's driver (e.g. byhaving observed the driver's past behaviour). Not all of the inputinformation is directly usable for the algorithm. For example, in termsof V2V communication, other vehicles are typically sending out theircurrent location and movements. However, as the optimisation algorithmis performing optimisation of the future vehicle actions, the V2Vinformation needs to be extended by a prediction of how other vehiclesare likely to behave in the future. Such a prediction may be done bymeans of formulating a set of rules that determines the predictedbehaviour, for example specifying that target vehicles should followspeed limits and keep a safe distance to their preceding vehicles.

The results of the optimisation may be used in a semi-autonomouslongitudinal control feature that directly actuates the optimized speedtrajectory and/or powertrain usage optimisation. In such a scheme, theoptimized speed and powertrain usage profiles are sent directly to acontroller that is responsible for final decision on the powertrainactions. The behaviour of other vehicles may differ from their predictedbehaviour, for example a target vehicle 15-n in front of the hostvehicle 1 may decelerate unexpectedly. In such a case the vehicle speedcontrol unit 20 may default back to a conventional radar-based ACC thatwould maintain a safe headway between the host vehicle 1 and the targetvehicle 15-n. Alternatively, or in addition, the optimisation resultscan be used is in a driver-advisory feature that recommends actions tothe driver who is in control of the longitudinal motion. In thisscenario, the optimised speed profile may be used to recommend actionsthat would be beneficial for energy efficiency, for example toaccelerate to certain speed or to lift off the accelerator pedal. Insuch a case, it is likely that there will be a difference between theoriginal optimized speed profile and the one resulting from the driveractions. It is therefore important that the optimisation results areadapted to the new situation, either with additional logic that comparesthe original planned trajectory and the actual one, or by simplyrerunning the optimisation.

It will be appreciated that various modifications may be made to theembodiment(s) described herein without departing from the scope of theappended claims.

1-35. (canceled)
 36. A method of generating a target operational speedband for a host vehicle travelling along a route, the method comprising:identifying a first time-dependent obstacle at a first location on theroute, the first time-dependent obstacle being identified as hinderingprogress of the host vehicle during a first time period; defining thefirst time-dependent obstacle in a two-dimensional speed againstdistance map; determining a first speed trajectory from a first point toa second point within the two-dimensional speed against distance map,the second point representing the first location on the route and thedetermined first speed trajectory representing the host vehicle arrivingat the first location at a first arrival time; and determining thetarget operational speed band such that the first speed trajectory formsone of an upper limit and a lower limit of the target operational speedband, wherein the first speed trajectory is generated for a firstacceleration limit of the host vehicle, and said first arrival time isoutside said first time period.
 37. A controller for generating a targetoperational speed band for a host vehicle travelling along a route, thecontroller comprising: processing means for receiving an input toidentify a first time-dependent obstacle at a first location on theroute, the first time-dependent obstacle being identified as hinderingprogress of the host vehicle during a first time period; and memorymeans connected to the processing means; wherein the processing means isconfigured to: define the first time-dependent obstacle in atwo-dimensional speed against distance map; determine a first speedtrajectory from a first point to a second point within thetwo-dimensional speed against distance map, the second pointrepresenting the first location on the route and the determined firstspeed trajectory representing the host vehicle arriving at the firstlocation at a first arrival time, the first arrival time being outsidethe first time period; and generate the target operational speed band;wherein the first speed trajectory forms one of an upper limit and alower limit of the target operational speed band; and the first speedtrajectory is generated for a first acceleration limit of the hostvehicle.
 38. The controller as claimed in claim 37, wherein the firstspeed trajectory forms the lower limit of the target operational speedband; and a cost penalty is applied to a target speed trajectory whichis less than the first speed trajectory.
 39. The controller as claimedin claim 37, wherein the first speed trajectory forms the upper limit ofthe target operational speed band; and a cost penalty is applied to atarget speed trajectory which is greater than the first speedtrajectory.
 40. The controller as claimed in claim 37, wherein theprocessing means is configured to determine a cost of a target speedtrajectory by applying an acceleration cost penalty in respect of eachportion of the target speed trajectory having an acceleration that isone of a positive acceleration greater than a predefined positiveacceleration threshold and a negative acceleration greater than apredefined negative acceleration threshold.
 41. The controller asclaimed in claim 37, wherein the processing means is configured toidentify a second time period during which the first time-dependentobstacle permits substantially unhindered progress of the host vehicle;and wherein the target operational speed band is determined such thatthe first arrival time is inside said second time period.
 42. Thecontroller as claimed in claim 37, wherein the processing means isconfigured to: determine a second speed trajectory from the first pointto the second point within the two-dimensional speed against distancemap, the second point representing the first location on the route andthe determined second speed trajectory representing the host vehiclearriving at the first location at a second arrival time; and determinethe target operational speed band such that the second speed trajectoryforms the other of the upper limit and the lower limit of the targetoperational speed band, wherein the second arrival time is outside saidfirst time period.
 43. The controller as claimed in claim 42, whereinthe first speed trajectory is generated for a first acceleration limitof the host vehicle.
 44. The controller as claimed in claim 37, whereinthe first obstacle comprises a target vehicle travelling along at leasta portion of the route.
 45. The controller as claimed in claim 44,wherein the first time period comprises a time period during which thetarget vehicle is predicted as travelling on a section of the routeidentified as being unfavorable for performing an overtaking maneuver.46. The controller as claimed in claim 45, wherein the processing meansis configured to: determine a second speed trajectory from the firstpoint to the second point within the two-dimensional speed againstdistance map, the second speed trajectory being calculated such that thehost vehicle arrives at the second location at a second arrival time,wherein the second speed trajectory forms the other of the upper limitand the lower limit of the target operational speed band.
 47. Thecontroller as claimed in claim 46, wherein the second arrival timecomprises a time that the target vehicle is predicted to arrive at thesecond location, the second location representing an end of the sectionof the route identified as being unfavorable for performing anovertaking maneuver.
 48. The controller as claimed in claim 37, whereinthe processing means is configured to identify a second time periodduring which the first time-dependent obstacle permits substantiallyunhindered progress of the host vehicle; the target operational speedband is determined such that the first arrival time is inside saidsecond time period; and the second time period comprises a time periodduring which the target vehicle is predicted as travelling on a sectionof the route identified as being favorable for performing an overtakingmaneuver.
 49. The controller as claimed in claim 37, wherein theprocessing means is configured to: identify a speed limit applicable forat least a part of the route between a current position of the hostvehicle and the first location, wherein the speed limit defines at leasta portion of the upper limit of the target operational speed band. 50.The controller as claimed in claim 37, wherein the processing means isconfigured to: identify a plurality of obstacles on the route; andgenerate a target operational speed band in respect of each obstacleidentified on the route.
 51. The controller as claimed in claim 50,wherein the processing means is configured to apply a weighting to thecalculation of each target operational speed band in dependence on thecalculation performed in respect of at least one other obstacleidentified on the route.
 52. The controller as claimed in claim 50,wherein the first arrival time for arriving at the first obstacle isdetermined in dependence on an arrival time of the host vehicle at oneor more other obstacle identified on the route.
 53. A non-transitorycomputer-readable medium comprising a set of stored instructions which,when executed, cause a processor to perform the method claimed in claim36.